Control system for scanning probe microscope

ABSTRACT

A control system ( 32, 75 ) is for use with a scanning probe microscope of a type in which measurement data is collected at positions within a scan pattern described as a probe and sample are moved relative to each other. The control system is used in conjunction with a position detection system ( 34 ) that measures the position of at least one of the probe and sample such that their relative spatial location (x, y) is determined. Measurement data may then be correlated with empirically-determined spatial locations in constructing an image. The use of empirical location data means that image quality is not limited by the ability of a microscope scanning system to control mechanically the relative location of probe and sample.

This invention relates to the field of probe microscopy and, inparticular, to a control system used to drive and monitor the relativepositions of a sample and microscope probe during the course of a scan.

The principle behind the scanning probe microscope (SPM) is to carry outa mechanical scan over a sample surface with a nanometric probe tip inorder to produce an image of the sample. Features within the imageresult from variations in an interaction between the tip and the sample.

A particular example of the SPM is the atomic force microscope (AFM) inwhich the force interaction between the sample and the sharp tip of aprobe is monitored. The present invention is applicable to all SPMs andthe AFM is described herein by way of example only. The probe of atypical AFM includes a very small cantilever that is fixed to a supportat its base and with the tip at its opposite (free) end. When the probetip is brought into close proximity with the sample, an interactionforce develops between sample and tip. If the tip is in motion, forexample oscillating, the interaction force will modify this motion insome way. If the tip is static, the force will displace the tip relativeto the sample surface.

During the course of a scan, the strength of the interaction between tipand sample surface will change as the characteristics of the surfacebeneath the probe tip change. A three axis high-resolution scannertypically generates relative motion between the sample and the probe,driving either the sample and/or probe support. The effect of theinteraction force on either the position and/or motion of the probe tipis monitored during the course of the scan. In standard AFM operation,the strength of the interaction force is held constant. That is, itseffect on the probe is observed and a feedback system operates to adjustthe separation of the sample and the base of the probe in response toany change so as to return the observed parameter to a predeterminedvalue, its set point. Data associated with this adjustment(conventionally, vertical or “z” movement) is collected and may be usedto construct an image of the sample across a region of its surface.

The interpretation of the image formed by the AFM will depend to someextent to the nature of the surface under investigation. Surfacetopography generally makes the most significant contribution to theimage, the height of the sample being closely followed by the probe asit scans, but other characteristics such as surface hydrophobicity andhydrophilicity, visco-elasticity, etc. may also contribute. The probeand microscope may further be adapted to measure other sampleproperties, such as magnetic or electric fields, via suitableinteraction forces.

AFMs may be designed to operate in a variety of imaging modes. Incontact mode the probe remains in substantially continuous contact withthe sample. In dynamic mode the probe is oscillated, bringing itperiodically into close proximity or contact with the sample.

If a static tip is used to probe the surface then interaction betweenthe tip and the surface is monitored during the course of a scan usingthe effect that the interaction force has on the bend or deflection ofthe cantilever. As the interaction force between tip and surfacechanges, the tip is either pulled towards or pushed away from thesurface. This tip movement is communicated to the cantilever part of theprobe, which accordingly bends or flexes along its length. The AFM isset to measure the deflection of the cantilever with a positionsensitive detector such as an optical lever system or other deflectiondetector as is well known in the art. Deflection, in this context,refers to the tilt of an upper surface of the probe, which is used bythe AFM to provide an indication of cantilever bend.

Alternatively, the AFM may be operated in dynamic mode. The probe istypically oscillated at or near one of its resonant frequencies.Variations in the sample-probe interaction affect the motion of theprobe. In particular, the amplitude, phase and resonant frequency ofthese oscillations may be monitored and probe-sample separation adjustedin order to maintain constant average interaction.

The AFM can be configured and used in many different modes. It should beborne in mind that the above description of contact and dynamic modes isto provide a general introduction to the particular field of atomicforce microscopy and is not intended to imply any limitation to thefield of application of this present invention in any way. Thisinvention is indeed suitable for use with any scanning probe microscopesystem.

Regardless of their mode of operation, AFMs can be used to obtain imageson an atomic scale of a wide variety of samples in a range ofenvironments (air, liquid or vacuum). Typically, they employpiezoelectric actuators, optical lever deflection detectors and verysmall cantilevers produced using silicon fabrication techniques. Theirhigh resolution and versatility has led to their finding application indiverse fields such as industrial inspection, semiconductormanufacturing, biological research, materials science andnanolithography.

Other scanning probe microscopes investigate other interactions betweena probe and sample surface. For example, scanning near-field opticalmicroscopes measure the optical near-field interaction between the tipand the sample; capacitance microscopes measure a capacitance developedbetween the sample and a metallic probe; scanning tunnelling microscopesmeasure the tunnelling current between a conductive tip and conductivesample. One thing that is common to all such microscopes however is thatthey effect a scan between probe tip and sample and that measurementsare taken at intervals during the scan. A range of probe types may beemployed: cantilevered, metallic, optically transmissive and a vastarray of samples may be investigated.

One problem that must be addressed by all such SPM systems is the needto correlate a measured value with the spatial (x,y) location at whichthat measurement is made. The x,y coordinates for each measurement areclearly dictated by the x,y scan pattern that is effected by themicroscope and the timing of sampling points during this scan. Eachmeasurement is accordingly taken at a particular spatial location andthis spatial location must be mapped to a corresponding location in theimage in order to construct an image of the surface. Each measurementspatial position generally corresponds to a pixel in the image.

It should be noted that absolute values of x and y are not necessary.What is needed is a knowledge of the relative positions of probe andsample in order to construct the image. Values are therefore maderelative to any convenient origin, for example the start position of thescan.

In order to derive the pixel locations, a microscope control systemgenerates a known signal that is input to the x,y scanners. For thepurposes of this example, the scanners are set to drive the probe acrossthe sample, but they could equally be set to drive the sample beneaththe probe. In response to the signal input, the scanners move the probemount to a known position. The control signal is varied such that theprobe (via its connection to the mount) is scanned across the samplearea to be imaged. At set intervals during the scan the microscoperecords the signal measurement at that point. As the trajectory of theprobe is known and the time intervals at which measurements are made,the spatial location of each measurement value is also known. Thecontrol system captures the measurements and uses the known spatialposition of the probe to locate these measurements in the image.

Recent advances in probe microscopy have led to much faster scanningtechniques with more rapid data collection times. With this newgeneration of microscope, such as that described in PCT patentapplications WO 02/063368 and WO 2004/005844, it is however becomingincreasingly apparent that constraints imposed by the microscopecomponents themselves are limiting image collection times.

In order to cope with these higher scanning speeds, alternativedetection systems have been developed that measure directly the verticalposition of the probe tip as it traces the surface of the sample. Thesystem described in WO 2009/147450 uses interferometry to measure theheight of the back of the probe above a reference level, for example thesurface of the stage. Measurement of the probe's vertical position ateach pixel location provides a direct indication of the topography ofthe sample. This is to be contrasted with the above-described the priorart AFM, which is a nulling system in that it is only required to holdthe probe orientation, monitored via its deflection, constant. In theprior art system, probe height information is obtained from the driversthat operate the feedback loop that ensures constant deflection.

As scanning speed increases, the ability of the x, y drivers to move theprobe along the requested trajectory and to the desired location isreduced. Inaccuracies in the ability to position the probe at thedesired location lead on to inaccuracies in pixel positioning in theimage. This reduces the quality of the image. In the prior art, closedloop scanners may be used to improve the ability of the microscope toposition the probe at the location requested by the control system. Theclosed loop scanning control system includes a sensor to monitor theposition of the scan stage (supporting probe or sample). The output ofthe sensor is included in a feedback loop, which adjusts the controlsignal input to the x,y scanners in order that the scanners reproducemore closely the motion that is requested by the control system.

Regardless of this closed-loop refinement however, the prior artapproach to determining the spatial location of a measurement positionis to drive the probe along a known trajectory and to collectmeasurements at set intervals along this trajectory. Measurementpositions and thus the positions of pixels in the image will thereforebe at correspondingly known spatial locations. This approach is limitedby the degree to which the true probe position corresponds to itstheoretical position, as demanded by the control system. That is, by theability to control the scanners mechanically such that they move to aknown position.

It is an object of the present invention to provide a control system foruse with a scanning probe microscope that provides an alternativedetermination of spatial location of an image measurement point, whichis not limited by the ability of the scanning system drivers tomechanically control the location of the probe or sample.

Accordingly, the present invention provides a control system for usewith a scanning probe microscope of a type in which measurement data iscollected at positions within a scan pattern described as a probe andsample are moved relative to each other. The control system is arrangedto set up an array of pixels, each pixel having an area that maps to afinite spatial area of the sample surface. For each measurementposition, a spatial location of that position is determined empiricallyand the value of a data point measured is associated with the pixelwhose mapping is to the sample area that includes theempirically-determined spatial location. The data values associated witha single pixel area are combined to determine a final data value forthat pixel position.

It can thus be seen that this approach differs markedly from the priorart. Prior art image collection systems are essentially dictated by theform of the image. That is, the image spatial characteristics aredetermined prior to data collection and the scanning system drives theprobe to collect data at each pixel point in the image. By way ofcontrast, the present invention makes no supposition as to where thescanning system drives the probe to take a measurement point. The probemay be driven freely and data points collected at any point along thetrajectory. All that is important is that each data point is collectedat a measured spatial location. When constructing the image, theconventional pixel array is used but it is only after data collectionthat the image is constrained to take this form. Oversampling can beused to improve the accuracy of the data value at the relevant pixel byallowing an average value to be generated for that pixel.

Although the probe may be driven freely, as specified above, thisrepresents only one implementation of this invention. More commonly, thecontrol system will drive the probe along a trajectory that approximatesa predetermined scan pattern, for example a raster scan. This inventionimproves on the prior art in that any deviation from the intendedtrajectory will not result in an error or inaccuracy in the image. It isclear therefore that the control system of this invention may be usedwith prior art microscopes, but additionally provides the capability ofremoving errors arising from incorrect positioning of the x, y scanner.

Two approaches may be taken for the empirical determination of probespatial location. First, the x and y coordinates of the probe may bemeasured directly. Secondly, and with reduced data processingrequirements, the system may be calibrated and a model constructed inwhich control system drive signal is mapped to probe spatial location.Thereafter, the model is used in order to predict probe spatial locationfrom a knowledge of the signal sent to the drivers.

There are a number of reasons as to why the actual motion generated by ascanner (or x,y drivers) may not follow the form of the signal that isdriving it. In the first place most SPMs employ piezoelectric drivers,whose operation is fundamentally based on the nonlinear piezoelectriceffect. In addition there may be hysteresis in the response, anomaliesdue to mechanical resonances in the system and other instabilities. Thisdeparture from a readily predictable scanning behaviour becomes moresignificant at fast scanning speeds and high-resolution imaging.

Closed loop scanners do offer noticeable improvement at low scan speeds,typically less than 10 Hz. However this means of correction becomes lesseffective at high scan speeds.

The control system may include a scanning system arranged to control atleast one of the probe or sample in order to change their relativeposition and a position detection system arranged to measure the spatiallocation of the at least one of the probe and sample that is controlledby the scanning system. Ideally, the position detection system includesan interferometer. Interferometry is an accurate technique by whichsmall displacements may be measured and, as such, is suited for use withthis invention.

In another aspect the present invention provides a method of imagingusing a scanning probe microscope, the method comprising the steps of:

-   -   (a) scanning a probe relative to a sample surface, the probe        comprising a nanometric tip in close proximity to the surface        and, at multiple data points during the scan, collecting image        data relating to an interaction between the probe and surface at        an empirically-determined spatial location;    -   (b) processing the data to generate an image in the form of a        pixel array, each pixel being mappable to a finite area of the        sample surface, wherein        -   (i) for each collected image data point, the value thereof            is assigned to a pixel location, the pixel being the one            that maps to the area of the surface that encloses the            empirically-determined spatial location of that data point;            and        -   (ii) for each pixel, combining the values assigned to that            location, thereby determining an updated data value for that            pixel position; and        -   (iii) constructing an image based on the updated data values            for the pixel positions.

The updated data value for one image data point may be incorporated inthe image prior to processing the next image data point. That is, datacollection and processing may be done in real time. Alternatively, themage may be constructed after processing multiple image data points, forexample all those collected within a selected sample area.

Embodiments of the invention will now be described by way of exampleonly and with reference to the accompanying drawings.

FIG. 1 is a schematic illustration of the components of an atomic forcemicroscope showing a scanning control system in accordance with thisinvention.

FIG. 2 is a schematic illustration of the components of an atomic forcemicroscope with an interferometric direct height detection system and asecond embodiment of a scanning control system in accordance with thepresent invention.

FIG. 3 is a flow chart illustrating the steps involved in constructingan image from data collected using a scanning control system inaccordance with this invention.

FIGS. 4 a, 4 b and 4 c show data points assigned to representative pixelarrays in construction of an image.

FIG. 1 illustrates the basic components of an AFM 10 operated using acontrol system in accordance with this invention. The AFM 10 comprises amoveable stage 12 on which a sample 14 to be investigated by a probe 16is mounted. The probe 16 comprises a cantilever beam 18 and a tip 20,which tapers to a fine point 20 a, and which is located towards one endof the cantilever beam 18. The other end of the cantilever beam 18 isfixed to a mount 22. A z-positioning system 24, comprising piezoelectricdrivers that are operable to move the stage 12 towards and away(z-direction) from the probe 16 is connected to the stage 12. An (x,y)scanner 25 is connected to either the mount 22, the stage 12 or both andincludes drivers that are operable to provide relative motion betweenthe sample 14 and probe 16 in the plane (x,y) of the sample. A lightsource 26 is arranged to emit a beam L which is directed onto an uppersurface (back) 18 b of the cantilever beam 18 at the position at whichthe tip 20 is mounted. Light reflected from the back 18 b of thecantilever propagates to a position sensitive detector (PSD), typicallya split photodiode 28, and a feedback signal is generated. The output ofdetector 28 is connected via a feedback controller 30 to thez-positioning system 24. A microscope control system 32 controlsoperation of the scanners (x,y scanner 25, z-positioning system 24) andalso captures measurement data in order to construct an image of thesample.

The feedback signal from the PSD may be processed to extract quantitiessuch as probe deflection, amplitude, phase or other parameters. Forsimplicity, this prior art AFM will be described as operating in contactmode using feedback based on probe deflection.

The microscope in accordance with the present invention, and in contrastto conventional AFMs, includes an x,y detection mechanism 34, which isarranged to obtain an indication of the spatial location of the probemount 22. Spatial location information, along with the feedback data, isinput to the control system 32 for analysis.

The probe 16 is generally (for AFM) fabricated from silicon or siliconnitride. Typically, the cantilever 18 is around 50-200 μm long, 20-50 μmwide and around 0.2-2 μm thick, but this size can of course be variedaccording to application. The shape may also be varied: typically it isrectangular or triangular with, in the latter case, the tip 20 at itsapex. The tip 20 is typically 5 μm at its base, 3-10 μm high and with anend radius of curvature of 10-20 nm. In use, the fine point 20 a at theend of the tip 20 is oriented towards the sample.

In taking an image of the sample, the prior art AFM 10 operates asfollows. Using the z-positioning system 24, the tip 20 is first movedtowards the sample 14 until the cantilever 18 deflects to apredetermined level. This predetermined degree of cantilever 18deflection, for example that indicated in FIG. 1 by probe outline P1, isthe set point for the feedback controller 30.

The deflection of the cantilever 18 is monitored using the light beam Land the detector 28. The detector 28 is split across its length intoindependent detector areas A and B. The output signal from the detectoris the difference between the intensity of light illuminating area A andthat illuminating area B. The intensity difference output from thedetector therefore provides an indication of cantilever deflection. Whenthe cantilever 18 is bent to position P1 the output from the detector 28is equal to the set point of the feedback loop.

The x, y scanner 25 is now operated to scan the tip 20 across thesurface of the sample 14, usually following a raster pattern. When thetip 20 encounters a part of the surface with increased height, the tip20, which traces the surface, is forced further upwards. This, in turn,causes the probe 16 to increase its flexion to, for example, positionP2. With the probe 16 in this position, the angle of incidence betweenlight beam L and the surface defined by the back 18 b of the cantileveris varied. Light L is accordingly reflected along a different path D2and is therefore incident more fully on area A of the detector than areaB. That is, the intensity difference I_(A)-I_(B) between light incidenton the two parts of the detector 28 has changed from its previous (setpoint) value. It can therefore be seen that the value of the intensitydifference provides an indication of the deflection of the cantileverand, importantly, an indication as to how far it has been deflected fromits set point. The feedback controller 30 is set to adjust the verticalposition of the probe mount 22 to move it away from the sample 14 and soto return the deflection signal received from the detector 28 to its setpoint. The probe 20 is accordingly maintained in the orientation shownas P1.

Conversely, when the tip 20 encounters a part of the surface withdecreased height, the bias on the cantilever beam 18 that results fromits set-point bending pushes the tip 20 downwards. The probe 16 willtherefore reduce its flexion and adopt an orientation such as thatindicated by P0. With this orientation, the angle of incidence betweenof light beam L on the back 18 b of the cantilever is such that the beamL is reflected along path D0. Area B of the detector is accordinglyilluminated more fully than area A. The feedback controller 30 againadjusts the vertical position of the probe mount 22 to move it towardsthe sample 14 and so to maintain the deflection signal at its set point.The probe 20 is accordingly maintained in the orientation shown as P1.In this way, the feedback of the microscope system operates continuouslyto ensures that the deflection of the probe 16, as determined by theangle of tilt of the back 18 b of the cantilever above the tip, is heldsubstantially constant during the course of a scan. This in turn ensuresthat the average interaction force between probe tip 20 and the sample14, which serves to attract or repel the tip to or from the surface, isalso held substantially constant. As the scan progresses, the verticalposition of the mount set by the z-positioning system is measured inorder to provide an indication of the height of the sample surface. Thisimage data is captured by the control system 32 for image constructionand analysis.

The x,y detection mechanism 34 includes an optical arrangement (notshown) that directs light from two different directions, in a planeperpendicular to the sample height measurement, onto the mount 22. Thesides of the mount are constructed to provide reflective surfaces innon-coplanar planes. A first beam of light is reflected from one of themount surfaces and input to an interferometer where it interferes with areference beam reflected from a reference (or x origin) point for thiscomponent. The second beam is similarly reflected from the second mountreflective surface and input to an interferometer for interference witha second reference beam reflected from a second reference (or y origin)point. From these two interferometric measurements the spatial locationof the mount 22 is extracted and input to the control system 32. As themount is in a fixed spatial relationship with the probe tip, thisprovides a measurement of the spatial location of the tip relative tothe sample. The control system thus receives or derives threemeasurements: the feedback signal indicative (for this AFMconfiguration) of the height of the probe (z) and the spatial locationcoordinates (x,y), which it processes to form an image.

As with the prior art, spatial location coordinates are only required todefine the position of the probe relative to the sample. This allowsflexibility in the selection of a suitable reference beam. In oneembodiment, the measurement beam may be reflected from, for example, theprobe and the reference beam from the sample stage. The interferencepatterns generated therefore provide a direct indication of the relativepositions of probe and sample. Moreover, this arrangement can be usedirrespective as to whether the x,y scanner 25 drives the probe, thesample or both.

Interferometric methods of extracting the path difference between twooptical beams are well known in the art and so will not be described inany further detail.

It is of course necessary to synchronise measurement of a data pointwith measurement of its spatial location. Various techniques may be usedto achieve this. A clock mechanism may be used to ensure that allmeasurements are collected at the same point in the scan. Alternatively,each individual measurement may be time stamped. Interpolation is thenused to provide the spatial location at the time of a particular datameasurement. Another option is to collect and process the data in realtime.

This technique to determine empirically the spatial location coordinatesof the probe as a sample measurement is taken differs significantly fromthe method of probe location known in the prior art. In a prior art SPM,the microscope control system generates a known signal that is input tothe x,y drivers. In response to this input, the drivers move the mount(or stage) to a known position. The control signal is then varied suchthat the probe is scanned across the sample area to be imaged, or samplescanned beneath the probe. At set intervals during the scan themicroscope records the signal measurement at that point. The controlsystem captures these signal measurements and uses the known spatialposition of the probe to construct the image.

In the above described embodiment of this invention, a full spatiallocation characterisation is carried out each time a scan is performed.That is, the spatial position of the probe is monitored continuously. Inan alternative embodiment, this characterisation is only carried out ina calibration phase. Calibration may be done as part of the scan or in apre-scan calibration phase. In the calibration phase, the control system32 is set to send a pre-determined drive signal to the x,y scanners 34.The response to the signal is determined by the interferometric spatiallocation measurement described above. A model is then constructedmapping drive signal to scanner response. In further data-gathering runsit is no longer necessary to measure spatial location directly. Providedthe same drive signal is used, it is sufficient to convert the drivesignal using the constructed model. This embodiment of the invention isparticularly useful in the case of a resonant scan in which one or bothof the (x,y) scanning drive mechanisms is replaced with a resonator. Theresonator is an oscillating drive set to oscillate the probe mount (orsample stage) at or near its resonant frequency. Such resonant scanningmicroscopes provide a very fast and stable scanning capability. Theresponse to a sinusoidal driving signal can be accurately modelled byderiving a phase shift and gain. The value of the shift and gain willvary from system to system, but it can be seen that only two parametersneed to be derived from the calibration phase in order to determinespatial locations for a range of driving signals. Additional parameterscan, of course, be used to model more complex forms of driving signal.

Whilst the above-described embodiment is less calculation-intensive,this advantage is gained with some loss in flexibility. In the firstembodiment described herein, there is no restriction on the drive signalprovided to the x,y scanner. That is, as no model is constructed thereis no need for the control system 32 to have any involvement withgeneration of the driving signal. This embodiment is thereforeinherently more flexible in its application to complex drivingmechanisms. Additionally, the performance of the first embodiment is notaffected by non repetitive variations in the relationship between thedrive signals to the scanners and the position of the probe.

As described above the x, y position of the probe is located by means ofinterferometric measurement of its mount position. Alternativelymarkers, for example in the form of a reflective cube, may beincorporated in the microscope system for the purpose of providing oneor more surfaces for measurement. Ideally, the marker would be locatedon the probe and the position of the marker measured. This is howeverdifficult to achieve practically. Preferably, the marker is placed nearthe base in order to minimise interference with the interaction betweentip and sample. Alternatively, the marker may be sited on the probesupport or at any other location that is in a fixed spatial relationshipwith the probe. If the sample is moved in order to generate the x,y scanthen the marker is placed on the sample stage. In another alternative, apair of markers may be used: one to reflect the reference beam and theother the measurement beam. If one marker is on the probe and the otheron the stage, a direct measurement of the probe/sample relative positionis provided. This implementation is advantageous in providing spatiallocations irrespective of whether the probe, sample or both are movedduring the scan. This may be particularly suited to the scanningmicroscope described above in which one or both of the (x,y) scanningdrive mechanisms is replaced with a resonator allowing, for example, onescan direction to be collected at probe resonance whilst the other iscollected by scanning the sample.

The spatial location measurements are not restricted to interferometricmethods. Any alternative device that is capable of measuring position toa sufficient degree of accuracy may also be used. Examples of suitabledevices for all position measurements are: capacitance sensor, linearvariable differential transformer (LVDT), optical lever and positionsensitive detector (PSD).

Turning now to FIG. 2 there is shown schematically an alternativeimplementation of a probe microscope, indicated generally by 70, that isparticularly suited for use with a control system constructed inaccordance with the present invention. Elements common to the AFMdescribed previously with reference to FIG. 1 are given the samereference signs. Accordingly, the microscope apparatus shown comprises amoveable stage 12 adapted to receive a sample 14, whose surface is to beinvestigated by a probe 16. The probe 16 comprises a cantilever beam 18and a tip 20, which tapers to a point 20 a, and which is located towardsone end of the cantilever beam 18. The other end of the cantilever beam18 is supported by a mount 22.

One or more drive motors (72, 73) are used to drive the sample 14(together with the stage 12) and/or the probe 16 such that they can bescanned relative to each other in three dimensions: x, y and zdirections. As is conventional in the field, the z axis of a Cartesiancoordinate system will be taken to be that perpendicular to a planeoccupied by the sample 14. That is, the strength of the interactionforce between probe 16 and sample 14 is dependent both on the xyposition of the tip 20 over the sample 14 (the pixel it is imaging), andalso on its height above it. The drive motors are categorised inaccordance with the direction in which they scan. A z-positioning system72 is operable to move the tip 20 towards and away from (z-direction)the sample 14. An x,y scanner 73 is operable in response to a signalfrom a control system 75 to provide relative motion between the sample14 and tip 20 in the plane (x,y) of the sample, such that the tip 20 isscanned raster fashion, or otherwise, over the sample 14.

In the embodiment shown both the z-positioning system 72 and the x,yscanners 73 are connected to the probe mount 22. The z-positioningsystem 72 may alternatively be connected to the sample stage 12 (asshown in FIG. 1). The x,y scanners 73 may also be connected to thestage. The drive motors 72, 73 are piezoelectric drivers. Alternatively,they may be based on non-piezoelectric driving mechanisms such as avoice coil or thermal bimorph actuator.

The probe 16 is a low-mass AFM probe and, during a scan, an interactionforce is developed between the tip 20 and the sample surface. A probedetection mechanism 74, which will be explained in more detail below, isarranged to obtain an indication of both the vertical (z) displacementof a point 18 b at the back of the cantilever above the tip 20 and itsdeflection (tilt). Data relating to the vertical displacement is outputto a system controller 75. Information relating to the tilt/deflectionof the back 18 b of the cantilever is input to a feedback controller 30,which in turn is connected to the drive mechanism of the z-positioningsystem 72.

As with the embodiment shown in FIG. 1, the x,y detection mechanism 34is arranged to obtain an indication of the spatial location of the probemount 22. Spatial location information, along with the previouslymentioned vertical displacement data, is input to the system controller75 for analysis.

Many alternative techniques may be used to derive a measurement of thelateral (x,y) position of the probe tip. In both the illustrated (FIGS.1 and 2) embodiments, the probe mount is monitored and its location usedto derive that of the probe tip. Alternatively, and as described inrelation to FIG. 1, the location of the probe may be observed directly,for example using light reflected from a reflective marker (not shown)fixed to the base of the probe. In fact, if the probe is scanned thenany point with a fixed spatial relationship to the probe tip, forexample the base or mount, may be used. In other SPM implementations theprobe is held stationary as the sample is scanned. In these embodiments,the position of the sample, or point in fixed spatial relationship withthe sample such as the stage, is measured during the course of a scan.

The probe 16 is generally (for AFM) fabricated from silicon or siliconnitride and formed to a shape and size as described previously inrelation to the prior art.

In taking an image of the sample, the AFM 70 operates as follows. Usingthe z-positioning system 72 and further drivers, the sample 14 is firstbrought into contact with the tip 20 at the start position of thespatial (x,y) scan. Conventionally, in AFM terminology, the tip 20 issaid to be in contact with the sample 14 when the atomic interactionforce is in the repulsive regime. Once the probe 16 makes contact withthe sample surface, the tip 20 is therefore pushed upwards. The base ofthe cantilever 18, at the side remote from the tip, is held in positionby the mount 22 and so the cantilever 18 is bent or deflected upwards.As is conventional, and as described in relation to the prior art, themount 22 is lowered, moving the probe 16 towards the sample 14 until thecantilever bend reaches a predetermined level. This predetermined levelis the set point for the feedback controller 30.

As the scan progresses, the tip 20 moves up and down as surfaceheight/interaction force varies. As it moves, the degree of tilt ischanged, which alters the signal fed to the feedback controller 30 andthe z-positioning system 72 is adjusted.

The operation of the direct height detection system will now bedescribed in more detail. A light source (not shown) emits a laser beam76 that is focused by objective lens 78 onto the back 18 b of thecantilever. Reflected light 80 a, b, c is collected by the lens 78 anddirected towards a non-polarising beamsplitter 82. As can be seen fromFIG. 2, the tilt of the cantilever 18 b affects the angle at which lightis reflected. If the probe is maintained at its set feedback position,the reflected beam follows path 80 b. If however, the cantilever back 18b is tilted leftwards (relative to the figure) the reflected beam 80 awill be deflected anticlockwise and a rightwards tilt will deflect thereflected beam 80 c clockwise. As the back 18 b of the cantilever islocated at or near the focal point of the lens 78, an angular variationin the reflected beam is converted to a lateral displacement after thelens. That is, regardless of angular tilt, the reflected beam 80 a, b, cwill propagate parallel to the optical axis of the detection system, aleftwards tilt producing a leftwards lateral displacement and arightwards tilt generating a rightwards displacement relative to the setfeedback position.

The beamsplitter 82 is arranged such that it reflects through 90°substantially half 84 a, b, c the light incident on it and transmits theother half 86 a, b, c. The transmitted component 86 a, b, c is input toan interferometer 88. In the interferometer, the reflected beam 86 a, b,c is interfered with a reference beam reflected from the upper surfaceof the stage 12. Alternatively, another fixed point with knownrelationship to the stage surface may be used. This provides a measureof the path difference between the two beams and hence an indication ofthe height of the back 18 b of the cantilever above the stage surface.Variations of this measured height are extracted and input to the systemcontroller 75 to form an image.

The components 84 a, b, c reflected from the beamsplitter 82 arecondensed by lens 90 onto a deflection detector 28. The detector 28 issplit across its length into independent detector areas A and B. Theoutput signals generated from these areas are input to a differenceamplifier 92, which outputs a signal equal to the difference between thetwo channels. The detector 28 is aligned with the collection optics suchthat when the cantilever back 18 b is tilted to its set deflectionposition, then the output from the difference amplifier will also be atits set point. That is, the reflected light 80 b, 84 b is distributedbetween channels A and B such that the difference in channel output is aset value. A leftwards tilt of the back 18 b of the cantilever meansthat the signal from the detector 28 increases in channel B, leading toa fall in output from the difference amplifier 92. Conversely, arightwards tilt means that channel A receives the signal increase and arise in output is generated by the difference amplifier 92. The feedbackcontroller 30 operates the z-positioning system 72 in order to maintainthe signal received from the difference amplifier 92 at its set point.

Independently of the feedback signal, or equivalently deflection of thecantilever, the true probe height above the surface is measured by theinterferometric height detection system. The feedback system isaccordingly used to ensure that the average deflection is maintained ata constant level.

It is important that the light 76 of the detection system is focused onthe back 18 b of the cantilever. For this reason, the z-positioningsystem is also connected to the objective lens 78 and arranged such thatif the probe 16 is raised or lowered, the lens 78 is raised or loweredby an equal amount. In an alternative embodiment, the objective lens 78is selected to have a depth of focus greater than the range of movementexpected from the tip. There is accordingly no need to adjust theposition of the objective with respect to the tip 20.

It is to be noted that although this detection system is described inrelation to an AFM, it can be used for all scanning probe microscopes,in which it is important to determine accurately the height of a probetip.

In this embodiment the x,y detection mechanism 34 and theinterferometric height detector of the probe detection system operate inmuch the same way, the main difference being that two separatemeasurements are required in order to derive x and y coordinates.Accordingly, the x,y detection mechanism 34 operates as described abovein relation to FIG. 1 The control system 75 of this embodiment receivesor derives three measurements: the height of the back of the probe (z)and the spatial location coordinates (x,y), which it processes to forman image.

As with the FIG. 1 embodiment, timings of x,y and z measurements aresynchronised by means of a clock mechanism, interpolation or otherwise.The full spatial location characterisation may be carried out for eachscan or only during a part of a scan, or in a pre-scan calibrationphase.

In the embodiments described above, each reference beam is arranged tohave a fixed optical path length relative to the x, y or z position ofthe sample. The reference beam for, for example, the z position couldaccordingly be reflected from the surface of the stage on which thesample is mounted or from a retroreflector whose position is linked tothat of the stage, as described above. Alternatively, the relationshipbetween reflector and sample z position does not have to be fixed. Insuch an embodiment the reference beam may be reflected from a fixedpoint, the fixed point having a known (but varying) relationship withthe z position of the sample. The height of the tip is therefore deducedfrom the interferometrically-measured path difference and the z positionof the sample with respect to the fixed point. Nor need the referencepositions for the x and y measurements (in any embodiment) remain fixed.A moving origin may be advantageous in eliminating systematic errors.

The interferometers described above are homodyne systems. Alternativeinterferometer systems, including heterodyne interferometers, capable ofmeasuring a change in optical path length, may also be employed withthis invention.

As before, the spatial location measurements are not restricted tointerferometric methods. A capacitance sensor, linear variabledifferential transformer (LVDT), optical lever and position sensitivedetector (PSD), among others, may alternatively be used.

Regardless of the details of the implementation, the control systems 32,75 in accordance with the present invention all received threemeasurements: one indicative of a measured parameter (the height of theback of the probe (z) in the AFM implementations described) and thespatial location coordinates (x,y), which are processed to form animage. With reference to FIG. 3, the steps involved in processing thesemeasurements to form an image will now be explained.

Image processing is carried out by first defining a pixel array(P_(m,n)), for example, 100 by 200 pixels. Each pixel of the image has afinite extent within the image and corresponds with a finite area of thesample surface. The resolution provided by the image processing systemis limited by the size of a single pixel. Example pixel arrays are shownin FIG. 4 and will be described in more detail below.

At step S10 measured values x_(n), y_(n) and I_(n) are read by thecontrol system 32 75. The symbol I_(n) is used as a representativemeasurement extracted by any scanning probe microscope system. It may bea height measurement extracted by an AFM such as those described above,an optical intensity measured by a scanning near-field opticalmicroscope, capacitance, magnetic force, surface viscosity or othermeasurement representative of a sample property or indeed any spatiallycorrelated measurement which is to be collected. The scope ofapplication of this control system will be apparent to one skilled inthe art.

If measurements are not simultaneous, then values x_(n), y_(n)corresponding to a particular I_(n) will not be known. In suchembodiments, a series of x and y measurements are taken at timeintervals t. The values x_(n), y_(n) at a time t₀ at which the value ofI_(n) is measured can then be found by interpolation.

In a still further alternative implementation, a series of x and ymeasurements are again taken at time intervals t. Once set values ofx_(n) and y_(n) are detected, then the microscope is instructed tomeasure a value of I_(n). That is, the microscope is scanned and thedata measurement collected at predetermined points.

In any case values of x_(n), y_(n) and I_(n) are input to or derived bythe control system 32, 75 for processing.

At step S12, for each data point collected by the system, its spatiallocation (x_(n), y_(n)) is found on an area of the sample surface thatmaps to a particular pixel, say P_(i,j). Accordingly at step S14, themeasurement information (I_(n)) is associated with pixel P_(i,j), readyto form the image. Each pixel P_(i,j) is associated with a count (countij), which is increased by 1 every time a value I_(n) is associated withthat pixel position.

At step S16 it is determined whether or not the scan has been completed.This may be the entire scan area, or only a part of the scan area thatmay be processed as data relating to further part-areas are collected toform the full image. If the scan is still in progress, or further dataawaits processing to form the image, then the method returns to step S10in order to process subsequent measured values of spatial location andimage parameter. If the scan is complete then, at step S18, ameasurement value is calculated from all of the I_(n) values that havebeen written to each pixel P_(i,j). This may be a straight arithmeticalaverage, by dividing by the current count ij value, as shown, or mayinvolve a more complicated mechanism to combine multiple values. At stepS20 the image is constructed with the averaged measurement valuedisplayed at each pixel position P_(i,j).

The contrast between this method of data collection and imageconstruction and prior art methods is apparent. In prior art systems,once P_(i,j) has been recorded, the scanner is directed to move to thenext pixel position P_(i+1,j) and the I_(n) measurement repeated. Thisnew data measurement is then written to pixel location and so on acrossthe array. In the present invention however, there is no set spatialrelationship between successive data measurements. If a firstmeasurement is at location (x1, y1) and the subsequent measurement atlocation (x1+δx, y1+δy), then, for anticipated sampling frequencies, itis likely that both (x1, y1) and (x1+δx, y1+δy) fall within the area ofthe sample that corresponds with the same pixel area P_(i,j). Thissituation is shown in FIG. 4 a. Alternatively, the second measurementmay fall within the range covered by P_(i+1,j), (see FIG. 4 b) orP_(i,j+1)(see FIG. 4 c). In any case, the new data measurement,regardless of any prior data measurements, is written to the pixel towhich it corresponds. When all data measurements have been distributedin the pixel array, pixels which hold multiple values are averaged tofind a single measurement value for that pixel.

As noted above, FIG. 4 shows three examples of pixel array patterns onwhich data sampling points (x1, y1) and (x1+δx, y1+δy) are overlaid. Itis apparent that different pixel arrangements may be used. Individualpixels may not be square, as shown by the array of FIG. 4 b, and thearray itself can cover an irregular area. Similarly all pixels may notbe constructed to the same resolution, i.e. spatial dimensions. In FIG.4 c a central area has a higher density of pixels in order to obtainhigher resolution at an area considered to be of more interest.

FIG. 5 shows an alternative embodiment of the data processing method ofFIG. 3 in which the averaging of pixel data is carried out in real timeas each measurement is added to the array.

Steps S10 and S12 proceed as for the first embodiment. That is, valuesx_(n), y_(n) and I_(n) are read by the control system 32 75 and thepixel P_(i,j) associated with spatial location (x_(n), y_(n)) isidentified. In this embodiment, the method then proceeds to step S22 atwhich the data value I_(ij) currently associated with pixel P_(i,j) isretrieved. If the count ij identifier is to be used in data combiningcalculations then it is also increased by 1 at this step S22. At stepS24 data averaging, or other form of combination is carried out. In itsmost general form, the data value I_(ij) is updated in accordance with acombining function ƒ that acts on the current value I_(ij) and the inputdata value I_(n). This combining function could be any of a number offunctions, for example a peak selection: I_(ij)=I_(n) if I_(n)>I_(ij)and I_(ij) otherwise, or an average:

$I_{ij} = \frac{{I_{ij} \times {count}\mspace{14mu} {ij}} + I_{n}}{{{count}\mspace{14mu} {ij}} + 1}$

Regardless of the mathematics used to effect the combination, the datavalue I_(ij) associated with pixel P_(i,j) is updated in accordance withall values so far measured at that pixel position. This value of I_(ij)is then displayed S26 at pixel position P_(i,j) in the image.

This embodiment of the invention is advantageous in that real-time dataprocessing and a continually updated display requires less storagecapability. At the high data collection rates anticipated for thisinvention, this is not an insignificant advantage. The same pixellocation may further be addressed multiple times. That is, if a samplearea requires further investigation, for example to improve resolution,then that particular area can be re-scanned in order to gather more datato write to the relevant selection of pixels.

The more data that is gathered during the scan, the better theresolution of the image. Not only will more pixels have multiplecontributions but the likelihood of blank regions appearing in the imageis reduced. For this reason the data collection rate is generally set tooversample the image. Data points are then reduced by averaging for eachpixel, which provides a tractable amount of data for further imageprocessing.

In a practical implementation of this invention, height measurements arecollected at a rate of 40 MHz. This amount of data is, in itself, verydifficult to store, review and analyse. The resolution available andhence sample area covered by a pixel is limited by the size of the probetip, which is of the order of a few nm. Assume that an area 1 μm by 1 μmis to be scanned in 1 second. If 10 nm resolution is available this is amaximum of 10000 sample points, and a frequency of 10 kHz is required.Thus the collection frequency actually oversamples in this instance by afactor of 4000, assuming a linear tip velocity. Data may be processed inreal time using, for example, a field gate programmable array (FGPA),which is well suited to this task.

Oversampling is also well suited to the collection of images using aprobe scanned at a non-constant probe velocity across the sample. Forexample, when using a mechanical resonance to generate the relativemotion between the probe and sample the scan velocity variesharmonically. A control system in accordance with this invention howevermay be used to generate an image that nevertheless has a constant pixelsize.

1. A control system for use with a scanning probe microscope of a typein which measurement data is collected at positions within a scanpattern described as a probe and sample are moved relative to eachother, wherein the control system is arranged to set up an array ofpixels, each pixel having an area that maps to a finite spatial area ofthe sample surface and, for each measurement position, a spatiallocation of that position is determined empirically and the value of adata point measured is associated with the pixel whose mapping is to thesample area that includes the empirically-determined spatial locationand wherein the data values associated with a single pixel area arecombined to determine a final data value for that pixel position.
 2. Asystem according to claim 1 wherein the spatial location of themeasurement position is measured directly during the course of a scan.3. A system according to claim 1 arranged to derive a model of spatiallocation from a signal used to drive a scanning system responsible formoving the probe relative to the sample, the model being derived fromdirect measurement of the spatial location of the measurement positionas the scanning system responds to the driving signal during acalibration phase.
 4. A control system according to claim 1 wherein thesystem includes a scanning system arranged to control at least one ofthe probe or sample in order to change their relative position and aposition detection system arranged to measure the spatial location ofthe at least one of the probe and sample that is controlled by thescanning system.
 5. A control system according to claim 4 wherein theposition detection system includes an interferometer arranged to measurespatial location.
 6. A system according to claim 4 wherein the scanningsystem controls the probe.
 7. A system according to claim 6 wherein theprobe incorporates a reflective marker located near to its base.
 8. Asystem according to claim 6 wherein the detection system measures thespatial location of the probe via observation of its mount.
 9. A systemaccording to claim 4 wherein the scanning system controls the sample.10. A system according to claim 9 wherein the detection system measuresthe spatial location of the sample via observation of a stage on whichit is mounted.
 11. A system according to claim 1 wherein the system alsoincludes a field programmable gate array or digital signal processorarranged to process measurement data in order to determine the finaldata values.
 12. A scanning probe microscope incorporating the controlsystem of claim
 1. 13. A scanning probe microscope according to claim 12wherein the control system includes a scanning system arranged tocontrol at least one of the probe or sample in order to change theirrelative position and a position detection system arranged to measurethe spatial location of the at least one of the probe and sample that iscontrolled by the scanning system and wherein the microscope alsoincludes a height detection system for detecting the height of the probein relation to the sample, both the height detection system and positiondetection system incorporating an interferometer.
 14. A method ofimaging using a scanning probe microscope, the method comprising thesteps of: (a) scanning a probe relative to a sample surface, the probecomprising a nanometric tip in close proximity to the surface and, atmultiple data points during the scan, collecting image data relating toan interaction between the probe and surface at anempirically-determined spatial location; (b) processing the data togenerate an image in the form of a pixel array, each pixel beingmappable to a finite area of the sample surface, wherein (i) for eachcollected image data point, the value thereof is assigned to a pixellocation, the pixel being the one that maps to the area of the surfacethat encloses the empirically-determined spatial location of that datapoint; and (ii) for each pixel, combining the values assigned to thatlocation, thereby determining an updated data value for that pixelposition; and (iii) constructing an image based on the updated datavalues for the pixel positions.
 15. A method according to claim 14wherein the updated data value for one image data point is incorporatedin the image prior to processing the next image data point.
 16. A methodaccording to claim 14 wherein the image is constructed after processingmultiple image data points.
 17. A method according to claim 14 whereinthe spatial location of the measurement position is measured directlyduring the course of a scan.
 18. A method according to claim 14 whereinthe spatial location of a measurement point is derived from a model, themodel being obtained by driving a scanning system responsible for movingthe probe relative to the sample in accordance with a drive signal,directly measuring the spatial location of the driven component (probeor sample) in response to this signal.
 19. A method according to claim14 wherein each step of collecting data is in response to the probebeing at a predetermined spatial location with respect to the sample.20. A method according to claim 14 wherein the step of combining thedata values assigned to each pixel location includes the step ofaveraging said values.
 21. A method according to claim 14 wherein thestep of combining the data values assigned to each pixel locationincludes the step of selecting the maximum of said values.